Question

Find the sum of first 20 terms of an A.P. whose common difference is 3 times the first
term and its 5th term is 25.​

Answer 1

Step-by-step explanation:

The idea behind the formula is that if you stack two arithmetic sequences, you get a nice rectangle. So with a simpler version of 1, 3, 5

2S = 1+3+5 + 5+3+1 = (1+5)+(3+3)+(5+1) = 3*6 for example.

The a and l are less important than the height of the rectangle, so adding the 5th and the 16th is the same as 1st and last in the initial question.

The sequence goes a, 4a, 7a … as we add three lots of the initial, so the fifth term is 13a. The 16th term is 46a so the height is 59a. This by the way is the same as a + (a + 19*3a) which would be first and last so…

Solving 5th term is 25

13a = 25, a = 25/13

So 2S = 20*59*(25/13)

And S = 10*59*(25/13)

Not a nice answer but hey.